Precision-based sizing finds the n that gives a confidence interval on a proportion a target half-width, by the Wald formula, which is conservative near p ≈ 0.5.
The Wald-formula n = z²·p·(1−p) / E² is maximised at p = 0.5, where the required n is largest. Using p = 0.5 as the planning value gives a conservative n that works for any true p.
For very small or very large expected p, Wilson-based formulas give tighter sample sizes; for routine planning, Wald with p = 0.5 is the safe default.
Expected p + target half-width E + confidence.
Required n.
Conservative defaults: use p = 0.5 to get the maximum required n unless you have a tighter expected value.